Study of Photoelectric Effect

The photoelectric effect is the observation that many metals emit electrons when light shines upon them. Electrons emitted in this manner can be called photo-electrons.

According to classical electromagnetic theory, this effect can be attributed to the transfer of energy from the light to an electron in the metal. From this perspective, an alteration in either the intensity or wavelength of light would induce changes in the rate of emission of electrons from the metal. Furthermore, according to this theory, a sufficiently dim light would be expected to show a time lag between the initial shining of its light and the subsequent emission of an electron. However, the experimental results did not correlate with either of the two predictions made by classical theory.

Instead, electrons are only dislodged by the impingement of photons when those photons reach or exceed a threshold frequency. Below that threshold, no electrons are emitted from the metal regardless of the light intensity or the length of time of exposure to the light. To make sense of the fact that light can eject electrons even if its intensity is low, Albert Einstein proposed that a beam of light is not a wave propagating through space, but rather a collection of discrete wave packets (photons), each with energy hf. This shed light on Max Planck’s previous discovery of the Planck relation (E = hf) linking energy (E) and frequency (f) as arising from quantization of energy. The factor h is known as the Planck constant :

The intensity of the radiation is given by the number n of transported packets

In the photoelectric effect a photon is completely absorbed by an electron, which increases its energy of an amount equal to hf

The kinetic energy of the emitted electrons is Ekin = hf – We

We = energy required to extract an electron from the material

hf = energy provided by the radiation

if hf <W → there is not enough energy in order to extract electrons → threshold

An electron can only receive energy from a quantum → the kinetic energy of the emitted electron does not depend on the intensity of the incident radiation

increasing the intensity of the radiation increases the number of packets of energy → the number of emitted electrons increases with the intensity

Ekin = hf – We → the energy of the single electron increases as the frequency of the incident radiation

The photoelectric effect provides evidence, in a way not related to the black-body radiation, that the electromagnetic radiation consists of quanta of energy hf.
These experimental facts can be easily verified by measuring the stopping potential V0, which is the electrical voltage needed to stop the flow of electrons generated by the effect photoelectric :

Ecin = hf – WeEcinmax = eV0V0 = ( hf – We )/e

The measurement should be done ​​at different wavelengths.
The values ​​of constants to be used :

h = 6.626×10-34 Jse = 1.602×10-19 Ch/e = 4.136×10-15 Js/C

Experimental Setup

For the experimental verification of the photoelectric effect, we used the setup described in the following diagram :

Setup Scheme

As phototube we used the model 1P39 characterized by an anode coated with Sb – Cs with spectral response of type S -4 , suitable for this type of use :